Question Detail
Question
If the value of α + β = 90° and α - β = 21°, then what is the ratio of sinα to cosβ?
Correct Answer
Option D is the correct answer.
Detailed Explanation
α + β = 90°, α - β = 21°. Adding: 2α = 111° → α = 55.5°, β = 34.5°. sinα = sin55.5°, cosβ = cos34.5° = sin(90°-34.5°) = sin55.5°. Therefore sinα = cosβ, so the ratio is 1:1.
Hint
Use complementary angle relationships: cosβ = sin(90°-β).